MASS DEFECT
By Prof. L. Kaliambos (Λ. Καλιαμπός) T. E. Institute of Larissa Greece April 16, 2016 Mass defect is the difference between the mass of a composite particle and the sum of the masses of its parts. It occurs not only in nuclear physics but also in the creation of atoms. MASS DEFECT IN ATOMS In the simplest case like the Bohr model (1913) the electrons can only gain and lose energy by jumping from one allowed orbit of radius r to another, absorbing or emitting electromagnetic radiation with a frequency ν'' determined by the energy difference of the levels according to the Planck relation: ΔΕ = hν where ''h is Planck's constant. During the transitions between energy levels, the electron of mass M and charge e in a way that cannot be pictured at a distance r (from the proton p of the same charge e), emits a photon (hν) regardless of the frequency f of orbital revolution of the electron. It is of interest to note that after my published paper " Nuclear structure is governed by the fundamental laws of electromagnetism ” (2003) the charge distributions in proton (5d = -5e/3 and 4u = + 8e/3) acting at a large distance of 0.529/1010 m = 0.529 x105 fm give a net point charge (+e). That is -5e/3 +8e/3 = +3e/3 = +e So according to the well-established electromagnetic laws the energy E of the electron is simply the sum of its kinetic energy mv2/2 and its potential energy -Ke2/r. Using the Coulomb law Mv2/r = Ke2/r2 we may write the equation for the energy of the electron in its orbit of radius r as E = -(1/2)Ke2/r Therefore when the electron “falls from infinity” to the ground state of energy E, Bohr could obtain exactly the experimental value in eV for the well known ionization energy E = 13.6 eV. That is the energy ΔΕ in eV can be written as ΔΕ = 0.5Κe/r = 13.6 eV Here K = 9 x109, e = 1.6/1019 Cb and r = 0.529/1010 m Evidently, when a photon with more energy than hν =13.6 eV needed to free the electron is absorbed, part of the energy is used to ionize the atom of hydrogen and the rest is given to the electron as kinetic energy KE= Mv2/2. We realize now that we have actually been speaking about the photoelectric effect as applied in 1905 by Einstein. Bohr in 1913 said: “Obviously, we get in this way the same expression for the kinetic energy of an electron ejected from an atom by photoelectric effect as that deduced by Einstein, that is KE = hν- W..” In general the magnitude of the ionization energy of an element is dependent on the combined effects of the electric charge of the nucleus, the size of the atom, and its electronic configuration. Among the chemical elements of any period, removal of an electron is hardest for the noble gases and easiest for the alkali metals. The ionization energy required for removal of electrons increases progressively as the atom loses electrons, because the positive charge on the nucleus of the atom does not change, and therefore, with each removal of an electron, the remainder are held more firmly. The ionization energy is often reported as the amount of energy (in joules or in eV) required to ionize the number of atoms or molecules present in one mole (i.e., the amount in grams of a given substance numerically equal to its atomic or molecular weight). However after my paper of dipole photons (1993) I showed that the photon absorption contributes not only to the increase of the electron energy ΔΕ but also to the increase of the electron mass ΔΜ in accordance with my discovery of the “Photon-Matter Interaction” given by hν/m = ΔΕ/ΔΜ = c2 It is of interest to note that Einstein in 1905 under his wrong hypothesis of massless quanta of fields developed his invalid relativity according to which the increase of the electron mass is due to the relative velocity of the electron with respect to a randomly moving observer. (See my “Correct explanation of photoelectric effect”). Also his invalid relativity led to the invalid mass-energy conservation which did much to retard the progress of atomic and nuclear physics. ( See my ENERGY DOES NOT TURN TO MASS). In fact, in hydrogen the absorption of photon energy hν needed to free the electron contributes to the increase of the electron potential energy ΔΕ. Therefore its kinetic energy of its orbit decreases from Mv2/2 to zero and this experimental situation invalidates dramatically the theory of special relativity. In the reverse case the interaction of a free electron of charge -e with the proton of charge +e leads to the creation of hydrogen (H) as e + p = H + hν In such an interaction the decrease of the electron energy ΔΕ becomes the energy hν of the photon, while the decrease of the electron mass ΔΜ (mass defect) becomes the mass m = hν/c2 of the emitted photon in accordance with my discovery of “Matter Matter Interaction” given by ΔΕ/ΔΜ = hν/m = c2 Historically, Newton was the first man who predicted the mass of particles of light confirmed in 1801 by the German mathematician Soldner. In the same way Einstein in his book “The Evolution of Physics" (1938) changed his previous ideas of 1905 and recognized that a photon has mass m = hν/c2. On page 234 of his book one reads: “A beam of light carries energy and energy has mass. But every inertial mass is attracted by the gravitational field, as inertial and gravitational masses are equivalent. A beam of light will bend in a gravitational field exactly as a body would if thrown horizontally with a velocity equal to that of light”. MASS DEFECT IN NUCLEI The "mass defect" can be explained also by using the above Matter Matter Interaction in the binding energies of nuclei. In my published paper of 2003 I showed that the binding energy is due to the electromagnetic interaction between nine charged quarks in proton and 12 ones in neutron. In the simplest case of the structure of deuteron D = p(+1/2)..n(+1/2) giving spin S =1 the electromagnetic interactions of the charge distribution (5d =-5e/3 and 4u = 8e/3) in proton (p) and the charge distribution (4u = 8e/3 and 8d = - 8e/3) in neutron (n) lead to the creation of deuteron after the emission of a photon of energy hν = 2.2246 MeV. This interaction is given by p + n = D + hν or p +n = p(+1/2)..n(+1/2) + hν Here the charged quarks are a part of 288 quarks in the new structure of protons and neutrons given by Proton = + 5d + 4u Neutron = +4u + 8d Note that the 93(dud) and 92(dud) give zero charge which cannot participate in the electromagnetic nuclear force. However the extra charged quarks 5d = -5e/3 of proton behave like a point charge at the center, while the 4u =+8e/3 are distributed along the periphery. On the other hand the same 4u= +8e/3 of neutron behaves like a point charge at the center, while the 8d = -8e/3 are distributed along the periphery. According to the differential equations of my paper of 2003 the electric interaction between the central charges and the peripheral charges give repulsive energies, while the electromagnetic interaction between the peripheral charges like the 4u of proton and 8d of neutron give an electromagnetic binding energy because the spin S=1 of deuteron contributes to the electromagnetic attraction. However the two repulsive electric energies are stronger than the one electromagnetic attraction. As a result the net Δw is a repulsive energy +Δw = + 1.5854 MeV. (See my “Simple nuclear force”). On the other hand the dominant electric binding energy -Εr (along the radial direction) between the two point charged quarks 5d of proton and 4u of neutron at the centers is very strong. It can be calculated by using the simple Coulomb law as -Εr = -K (5d)(4u)/r where r = 2R = 1.68/1015 m Since 5d = -5e/3 and 4u= +8e/3 we may calculate the binding energy in MeV as -Εr = - 9(109)(40/9) (1.6/1019)(1015/1.68) = -3.81 MeV Therefore the repulsive energy (+Δw) which contributes to the force of short range could be given also by +Δw - 3.81 = - 2.2246 or +Δw = 3.81- 2.2246 = + 1.5854 MeV In general the binding energy of deuteron ΔΕ = -Εr +Δw = -3.81 + 1.5854 = -2.2246 MeV is the total strong electromagnetic binding energy of deuteron. Therefore according to my discovery of Matter Matter Interaction the above electromagnetic binding energy of 2.2246 MeV becomes the energy hν = 2.2246 MeV of the emitted photon, while the mass defect ΔΜ = 2.2246 ΜeV/c2 becomes the photon mass m = hν/c2 = 2.2246 MeV/c2. (See my “Discovery of photon mass”). Here we see that the binding energy of deuteron ( -2.2246 MeV) is much more greater than the ground state energy of Hydrogen (-13.6 eV) because the charged quarks of proton and neutron interact at the very short distance 2R = 1.68/1015 m. The latter case is similar to the case with nuclei such as helium: to break them up into protons and neutrons, one must inject energy. In this case the binding energy between protons and neutrons is stronger than the repulsive energy between the identical protons. On the other hand, if a process existed going in the opposite direction, by which hydrogen atoms could be combined to form helium, then energy would be released. For elements heavier than oxygen, the energy that can be released by assembling them from lighter elements decreases, up to iron. For nuclei heavier than iron, one actually releases energy by breaking them up into 2 fragments. That is how energy is extracted by breaking up uranium nuclei in nuclear power reactors. The reason the trend reverses after iron is the growing net positive charge (+e) of the protons. In this case the charge distributions acting at greater distances behave like point charges of charge (+e) given by +e = [ 93(dud) +5d +4u] = - 5e/3 +8e/3 = +3e/3 So the electric force between protons may be weaker than the electromagnetic binding energy between protons and neutrons. In an iron nucleus, each proton as point charge repels the other 25 protons, while the electromagnetic binding energy between protons and neutrons only binds close neighbors in which interact the nine charged quarks in proton and the twelve charged quarks in neutron. As nuclei grow bigger still, this disruptive effect becomes steadily more significant. By the time polonium is reached (84 protons), nuclei can no longer accommodate their large positive charge, but emit their excess protons quite rapidly in the process of alpha radioactivity—the emission of helium nuclei, each containing two protons and two neutrons. (Helium nuclei are an especially stable combination.) Because of this process, nuclei with more than 94 protons are not found naturally on Earth (see periodic table). The isotopes beyond uranium (atomic number 92) with the longest half-lives are plutonium-244 (80 million years) and curium-247 (16 million years). It is indeed unfortunate that today many physicists influenced by Einstein’s invalid mass-energy conservation continue to believe that the nuclear phenomena could be explained by converting the mass defect into energy. MASS DEFECT IN THE ELECTRON- POSITRON INTERACTION In the same way, in the correct annihilation of the charge-charge interaction of the electron-positron system the energy ΔΕ= 1.022 MeV due to the interaction of charges (-e) and (+e) turns to the energy 2hν = 1.022 ΜeV and the mass defect ΔΜ = 2Μ = ΔΕ/c2 =1.022MeV/c2 turns to the photon masses 2hν/c2. In this case using in eV the Coulomb potential ΔΕ = Ke/r one finds that the two particles could be transformed into photons at the very small separation r = 1.41/1015 m . In fact, this situation shoud occur at a greater separation ( r > 1.41/1015 m ) because of the magnetic attractions due to the spins. Historically, in 1932, Anderson discovered the tracks of electron positron pairs created by a beam of energetic photons incident on a thin metal plate. The inverse, “pair annihilation” occurs whenever an electron and positron annihilate. However the explanation of this phenomenon was based incorrectly on the Einstein invalid mass-energy conservation. It is of interest to note that a large number of experiments showed that the fields of Maxwell and the relativity of Einstein are invalid theories because they violate the two conservation laws of energy and mass. So to avoid such wrong theories I presented at the international conference “Frontiers of fundamental physics” (1993) my paper of dipole photons. Surprisingly such dipole photons led to my discovery of the Photon-Matter Interaction which invalidates the electromagnetic theory of Maxwell and the theory of special relativity, because the dipole photons having mass in the correct explanation of photoelectric effect contribute not only to the increase of the electron energy ΔΕ but also to the increase of the electron mass ΔΜ. Einstein, under his false massless quanta of fields, and the wrong rest mass, violated the two conservation laws of energy and mass by introducing the invalid mass-energy conservation. Einstein himself pointed out: “Pre-relativity physics contains two conservation laws of fundamental importance, namely, the law of conservation of energy and the law of conservation of mass; these two appear there as completely independent of each other. Through relativity theory they melt together into one principle.” Although laws and experiments invalidate fields and relativity, today many physicists influenced by Einstein’s invalid special relativity believe that the mass of the two particles, in the so-called annihilation, turns to the energy of the Einstein false massless quanta of fields. For example in the “Annihilation-WIKIPEDIA” (in chapter electron-positron annihilation) one reads : “When an electron and a positron collide to annihilate and create gamma rays, energy is given off. Both particles have a rest energy of 0.511 mega electron volts (MeV). When the mass of the two particles is converted entirely into energy, this rest energy is what is given off. The energy is given off in the form of the aforementioned gamma rays.” Here we see that the fundamental electromagnetic interaction of these particles is absent. Instead it is used the wrong rest mass and the invalid rest energy. So ,to explain the correct pair annihilation I present here a brief history of my discoveries of Photon-Matter Interaction and Matter Matter Interaction able to interpret correctly the annihilation of electron and positron under the two conservation laws of energy and mass. After the experiment of the two American physicists French and Tessman (1963) who sowed the fallacy of Maxwell’s electromagnetic theory in favor of Newton’s rectangular particles of light ( confirmed by Soldner in 1801) and also after the the recognition of J.J Thomson that the electromagnetic energy is equivalent to the so-called “electromagnetic mass” used by Kaufmann for the explanation of his experiment (1901), I presented in 1993 by paper of dipole photons which led to my discovery of the Photon- Matter Interaction hν/m = ΔΕ/ΔΜ = c2 According to that discovery the interaction of a dipole photon with the charge (-e) of the electron in terms of the vectors Ey and Bz can be written as Ey (-e) dy = dw and Bz(-e)dy = Fm dt = dp = cdm. Since Ey/Bz = c we get dw/dm = c2 = hν/m Note that such a result under the application of Newton’s laws led to my discovery of length contraction and time dilation because the hypothesis of length contraction and time dilation introduced by Einstein leads to complications. For example Einstein in his invalid special relativity believed incorrectly that the simultaneity of Newton’s third law is not invariant but depends on the reference frame. Under such fallacious ideas I examined carefully the Kaufmann experiment and I discovered that according to the Photon-Matter Interaction or Photon Absorption the increase of the electron mass is due to the absorption of both energy and mass. Indeed, in the Kaufamnn experiment (1901) under the same length contraction and a time dilation the absorption of energy by an electron contributes not only to the increase of the electron energy ΔΕ but also to the variation of the electron mass starting from the Newton inertial mass Mo (before the absorption). Here we do not use the wrong rest mass and the invalid relativistic mass because they lead to complications. Instead we use Newton’s the constant nertial mass Mo (before the absorption) which is always constant in a mechanical conservative system where the sum of the kinetic and potential energy is constant as in gravity. Whereas, after the absorption we use a variable mass M in accordance with the following equation M2/Mo2 = c2/(c2-u2) Indeed the differentiation of this equation under the application of Newton’s second law leads to my discovery of the Photon-Matter Interaction as M2c2 = M2u2 Or 2MdM c2 = 2MdM u2 + 2uduM2 Or dMc2 = (dMu + udM)u = d(Mu)/dtds = (dp/dt)ds = dW This result deduced from the application of Newton’s second law invalidates dramatically the theory of special relativity. ( See my “Newton invalidates Einstein”). This photon absorption is a weak electromagnetic interaction similar to the weak electromagnetic interaction of the antineutrino absorption which invalidates the electroweak theory of the so-called weak interaction. (See my “Neutrino-Quark Interaction”). Category:Fundamental physics concepts